4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 2.0 L. The amount of heat absorbed in this expansion is ____________ L atm.

Solution

Chemistry ma’am · 3 steps

Expansion into vacuum pushes against nothing, so no work is done and no heat is needed.

1. No opposing pressure. In a vacuum pₑₓₜ = 0. Work of expansion is w = -pₑₓₜΔ V, so w = 0 whatever the change in volume.
2. Isothermal ideal gas. The internal energy of an ideal gas depends only on temperature. The temperature stays constant, so Δ U = 0.

   Δ U = q + w ⇒ 0 = q + 0

3. So. The heat absorbed is q = 0 L atm. The actual volumes play no part, because pₑₓₜ = 0 makes the work zero for any Δ V.

The idea to keep. Free expansion means pₑₓₜ = 0, so w = 0. For an ideal gas at constant temperature, Δ U = 0 as well, so q = 0 too.

Answer from the NTA final answer key. Solution by PrepWiser.